Hering's laws state that the perceived direction of binocular objects is an average of their two monocular directions referred to the cyclopean eye. These laws fail to describe perceived direction where surfaces overlap and an unpaired region of the occluded surface is created. Erkelens et al Vis Res (1996) proposed that in the neighbourhood of these occlusions, directions are perceived from the perspective of the eye with the unpaired region rather than in an averaged direction. In evidence they showed that binocular lines close to the unpaired region of a background surface appeared aligned with the edge of the occluding surface when actually aligned according to the eye seeing the unpaired region. However the stimulus conditions fostering uniocular determination of perceived direction are little explored. In our first experiment the stimulus was a textured occluding square (98') placed stereoscopically nearer than and central to a textured background. Observers vertically aligned a binocular line on the background with a fixed binocular line on the occluding surface. Alignment was an average of the monocular directions when the separation of the fixed line from the occluding edge was greater than approximately half the unpaired region's width and uniocular for smaller separations. Alignment between the vertical edges of the square's outline and the background line was found to be determined uniocularly even when both surfaces were devoid of texture. However when the horizontal edges of the textureless square's outline were removed, alignment was consistent with direction averaging. These results localise the transition from averaged to uniocular direction to a small area adjacent to the unpaired region and indicate that the presence of an occluding surface rather than unpaired texture determines that direction is uniocular near unpaired regions. Further research indicates that the orientation of the occluding edge may also be critical.